WTF is "trans-identifying"? They are not literally identifying as "trans". They are identifying as men/women (although the opposite of their biology), not as "trans". "Trans" is a description for people who identify as other than their biological sex; it is not an identity, per se.
You can doubt whether a trans woman is "really" a woman. But you cannot doubt that a trans woman is "really" trans. Trying to be the opposite of your biological sex is what "trans" literally means.
It makes as much sense as replacing "tall people" with "tall-identifying people".